{
  "id": "1012.5290",
  "version": "v3",
  "published": "2010-12-23T20:24:47.000Z",
  "updated": "2011-01-22T08:20:55.000Z",
  "title": "The Gardner equation and the L^2-stability of the N-soliton solution of the Korteweg-de Vries equation",
  "authors": [
    "Miguel A. Alejo",
    "Claudio Muñoz",
    "Luis Vega"
  ],
  "comment": "19 pages, final version incorporating referee's comments. To appear in TAMS",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Multi-soliton solutions of the Korteweg-de Vries equation (KdV) are shown to be globally L2-stable, and asymptotically stable in the sense of Martel-Merle. The proof is surprisingly simple and combines the Gardner transform, which links the Gardner and KdV equations, together with the Martel-Merle-Tsai and Martel-Merle recent results on stability and asymptotic stability in the energy space, applied this time to the Gardner equation. As a by-product, the results of Maddocks-Sachs and Merle-Vega are improved in several directions.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-01-22T08:20:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q51",
      "35Q53",
      "37K10",
      "37K40"
    ],
    "keywords": [
      "korteweg-de vries equation",
      "gardner equation",
      "n-soliton solution",
      "energy space",
      "gardner transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1012.5290A"
    }
  }
}